A shock appeared to be on the cards when Antony Sweeney scored his 10th goal of the season with the last kick of the first half.
But quickfire goals from youngster Piero Mingoia - on his senior debut - and Sordell put the Hornets in command midway through the second half.
Sordell made it 11 for the campaign with eight minutes remaining before substitute Danny Graham secured the in-form Hornets a sixth straight win at the death.
Watford made five changes, with Troy Deeney starting in attack as Graham was only deemed fit enough for a place on the bench. Rene Gilmartin was in goal, with regular shot-stopper Scott Loach among the substitutes.
Hartlepool dropped Steve Haslam, with Gary Liddle moving from midfield to partner Peter Hartley in the centre of defence. Midfielder Paul Murray came into the starting line-up, with Ritchie Humphreys playing as a lone striker.
The youthful Hornets side started brightly, with Deeney seeing a shot blocked by Evan Horwood and Martin Taylor heading wide from a Mingoia corner.
Pools, who went into the game having snatched four 1-0 wins on the road this season, had their first chance of the afternoon in the 22nd minute, but leading scorer Sweeney dragged his effort wide.
Humphreys flashed an effort inches past the post shortly afterwards as the League One side started to get a foothold in the game.
Deeney was wasteful from inside the area, while at the other end, lively winger Andy Monkhouse let fly from 25 yards but his attempt failed to trouble Gilmartin.
Mick Wadsworth's men took the lead in first-half injury-time when Sweeney was sent clear one-on-one with Gilmartin, and the midfielder coolly slotted home.
It was Hartlepool who began the second half strongly, with Leon McSweeney heading a Horwood cross wide before the same player cleared the crossbar with a shot from the edge of the box.
Humphreys was withdrawn after 62 minutes, with James Brown entering the action, and it should have been 2-0 to Pools moments later.
The ball fell kindly for Joe Gamble six yards out, but his fierce drive was brilliantly saved by Gilmartin.
Watford levelled in fine style from their next attack. Mingoia collected the ball by the left corner flag and cut inside before lashing the ball into the top corner.
The game was turned on its head two minutes later when Sordell found space in the area to send a right-footed shot into the bottom corner.
The Hornets' passage into the next round was sealed in the 82nd minute when Sordell neatly converted a Dale Bennett pass from six yards.
But there was still time for substitute Graham to add a fourth with a fine finish into the top corner from just inside the area.